Partially Ordered Set - Linear Extension

Linear Extension

A partial order ≤* on a set X is an extension of another partial order ≤ on X provided that for all elements x and y of X, whenever, it is also the case that x ≤* y. A linear extension is an extension that is also a linear (i.e., total) order. Every partial order can be extended to a total order (order-extension principle).

In computer science, algorithms for finding linear extensions of partial orders (represented as the reachability orders of directed acyclic graphs) are called topological sorting.